Our systems are now restored following recent technical disruption, and we’re working hard to catch up on publishing. We apologise for the inconvenience caused. Find out more

Recommended product

Popular links

Popular links


Algebraic Geometry and Statistical Learning Theory

Algebraic Geometry and Statistical Learning Theory

Algebraic Geometry and Statistical Learning Theory

Sumio Watanabe, Tokyo Institute of Technology
August 2009
Available
Hardback
9780521864671
£80.00
GBP
Hardback
USD
eBook

    Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory on algebraic varieties.

    • Presents a new statistical theory for singular learning machines ● Mathematical concepts explained for non-specialists ● Intended for any student interested in machine learning, pattern recognition, artificial intelligence or bioinformatics

    Product details

    August 2009
    Hardback
    9780521864671
    300 pages
    233 × 155 × 20 mm
    0.56kg
    13 b/w illus.
    Available

    Table of Contents

    • Preface
    • 1. Introduction
    • 2. Singularity theory
    • 3. Algebraic geometry
    • 4. Zeta functions and singular integral
    • 5. Empirical processes
    • 6. Singular learning theory
    • 7. Singular learning machines
    • 8. Singular information science
    • Bibliography
    • Index.
    Resources for
    Type
    Author's web page
      Author
    • Sumio Watanabe , Tokyo Institute of Technology

      Sumio Watanabe is a Professor in the Precision and Intelligence Laboratory at the Tokyo Institute of Technology.